The Gradient of a River: Bimetallism as an Implicit Fluctuation Band

Marc Flandreau, Centre National de la Recherche Scientifique

NOTE: The summary which appeared in the October 1997 issue of The Newsletter of The Cliometric Society contained graphics and formatting which cannot be accurately reproduced in this version.

One century and one year after its defeat in the 1896 US presidential election, bimetallism remains a disputed topic. A majority view holds that this regime was unstable, with repeated switches to de facto gold or silver monometallism reflected in movements of the gold-silver exchange rate on international bullion markets. By contrast Friedman ([1990a] and [1990b]), and Flandreau ([1996a] and [1996b]), have claimed that bimetallism could in time prove very robust. According to this minority view, France effectively succeeded in stabilizing the gold-silver price ratio on world markets, and might even have continued to do so had not French policy makers put an end to the free coinage of silver in 1873 (Flandreau [1996a]).
Part of the difficulty of reconciling these conflicting judgments comes from the record of the gold-silver price ratio itself. On the one hand, a bird's eye look shows that in London (admittedly the main bullion market of the time) the gold-silver price ratio experienced only modest fluctuations (say about 2% each way) around the French legal ratio of 15.5 to 1: this provides support to the stability view. But on the other hand, if we use a magnifying glass to track movements of the price ratio, we find long periods where the gold-silver price ratio remained, slightly but persistently, either above or under the legal ratio, and almost no period where it remained at the legal ratio. On the surface, this appears to be consistent with the claim that the bimetallic system was a "knife-edge" that repeatedly collapsed to de facto (gold or silver) monometallism (Garber [1986], Garber and Weisrod [1992], Oppers [1992]).
In this paper, which continues a controversy initiated during the 1995 Cliometric Society ASSA meetings in Washington, we offer a theoretical reconciliation of these contradictory stylized facts, focusing on the operation of the international monetary system between 1848 and 1873, the "heyday" of France's bimetallic system. Our analysis is consistent with the (minority) "stability" view. Our key insight is that taking into account the existence of arbitrage costs - a feature that has been regrettably excluded from all formal analyses of bimetallism - dramatically modifies the conventional analysis of bimetallic regimes.
Because shipping bullion is costly, exchange rates between bimetallic nations and gold nations can fluctuate within "gold points". Similarly, bimetallic exchange rates vis--vis silver nations may fluctuate within "silver points" (Flandreau [1996b]). This generates an implicit "target zone" for the gold-silver price ratio. This paper is the first attempt to model (and solve for) the behavior of the gold-silver price ratio within this indirect currency band. We show that the gold-silver exchange rate exhibits empirical features that have been incorrectly interpreted as evidence supporting the "knife-edge view" that bimetallism was unstable. We argue that they should instead be taken as an index of stability.

I. The State of the Art: Questions Answered and Unanswered
In the paper, we consider a simplified setting that matches the state of international monetary affairs as it prevailed prior to 1873 (Flandreau [1996a] and [1996b]). We have three countries: France, England, and Germany. France operates a fixed bimetallic ratio of 15.5 to 1; Germany is on silver; England is on gold. Money supplies are subject to exogenous gold and silver shocks, that have potentially destabilizing effects for the gold-silver price ratio.
These money supply shocks, however, may be buffered through the agency of the bimetallic economy. The argument for this was first formalized in the works of Walras [1881] and Fisher [1894]. In their view, bullion supply shocks are absorbed through stabilizing interventions. For instance, gold supply shocks are cushioned by a reallocation of currency holdings, French agents buying and coining gold, and financing the operation by melting and selling part of their holdings of silver francs: this operation has come to be known as "bimetallic arbitrage" (Friedman [1990a] and [1990b]).
However, if gold (resp. silver) supply shocks occur repeatedly, silver (gold) is gradually driven out of the French circulation. Eventually, a point is reached where the bimetallic country finds itself on a de facto gold (silver) standard. A bimetallic country can thus end up in one or the other of the three following regimes: effective bimetallism (where the gold-silver price ratio is equal to the legal ratio), de facto gold standard (with a price ratio below the legal ratio), or de facto silver standard (with a price ratio above the legal ratio).
These results are well known and very robust, although Walras' pioneering model was one of static general equilibrium, and Fisher's analysis ignored expectations. Yet their conclusions may be shown to hold in a dynamic framework with random money supply shocks and rational, forward looking agents. The only difference is that the collapse of bimetallism to de facto monometallism takes place sooner than in Walras' or Fisher's models (Oppers [1992]). The intuition underlying this claim is the familiar insight of speculative attack theory (Salant and Henderson [1978], Krugman [1979]). Gold (resp. silver) supply shocks, although buffered through arbitrage, increase the prospect of an eventual collapse of the bimetallic economy to a de facto gold (silver) standard. When this happens, silver (gold) appreciates. Thus rational agents discount this risk and buy silver (gold) for speculative purposes. Hence gold (silver) supply shocks drive more silver (gold) out of the bimetallic circulation than would occur with myopic agents, and the collapse to monometallism takes place earlier.
This emphasis on expectations has backlashed in a new knife-edge view, according to which the observed movements of the gold-silver price ratio away from the legal ratio are evidence that such frequent collapses occurred. In a paper presented at the 1995 ASSA meetings of the Clio, Oppers [1994] suggested that looking at the pattern of correlations between sterling exchange rates could serve to determine the effective regime prevailing in France at a given time. Intuitively, if the franc and mark exchange rates in terms of the pound behaved "in the same manner", this would indicate that the bimetallic country was on a de facto silver standard (for its currency would be like a silver currency). By contrast, a weak correlation would reveal that the bimetallic economy was on a de facto gold standard. Applying this methodology to the period following the California gold discoveries, Oppers argued that France switched from bimetallism to de facto gold monometallism in 1859.
Ron Michener who discussed Oppers' paper was critical. Among other things, he pointed that the empirical record regarding the quantities of specie held in France was at odds with Oppers' story (see also Flandreau [1995]). Indeed looking at the evolution of gold and silver holdings in France between 1840 and 1870 (a period during which France had to weather a gold glut and the onset of a silver shock) one fails to identify these dramatic switches from a predominantly silver to a predominantly gold circulation which Oppers claimed were implied by price movements.
Oppers replied that the existence of positive holdings of both metals did not mean per se that bimetallism remained effective in France, as silver might instead have been held for speculative purposes, in anticipation of a further collapse in the price of silver. This argument however is not convincing, given the extreme stability of the gold-silver price ratio (during the 1850s and 1860s it never fell by more than 2% under the legal ratio). Such a stability would have implied a low value for the option of selling silver, so that silver hoarding must have been consistently limited, a fact which is inconsistent with the large silver holdings kept in France in the 1860s. This is the essence of a quote by Viner [1937] who reported that contemporaries held that "variations in the market price of silver [in terms of gold] were too slight to compensate private concerns for holding it in stock". Indeed, had investors purchased French or British bonds (whose annual return was somewhere around 4%) they would have fared substantially better. It could mean that agents systematically overestimated the possibility of a downward jump in the price of gold: this, however, is highly unlikely given that the discovery of the Comstock silver load in 1859 meant that silver production was about to rise, thus further reducing the prospect for silver appreciation. Barring irrationality, we must conclude that silver specie in the 1860s was held for transactions, and that bimetallism remained effective in France. But how to explain, then, the observed tendency of the gold-silver price ratio to drift away from the legal ratio, while at the same time remaining in its vicinity?

II. The Model
Our claim is that the main flaw of the knife edge view is that by ignoring arbitrage costs, it is led to interpret every variation of the price ratio away from the legal ratio as evidence of a collapse to de facto monometallism. But in Flandreau [1997] we demonstrated that the spread between the price ratio and the legal ratio over the period 1850-1870 was always smaller than the cost of arbitraging away discrepancies between the two. The paper builds on this insight and constructs a model of bimetallism which recognizes that the business of shipping bullion involved expenses. The model is then shown to exhibit a number of features which are fully consistent with the historical record of bimetallism.
Recall that exchange rates between bimetallic France and gold based England could thus fluctuate within gold points. Symmetrically, exchange rates between Paris and Germany's main FX center, Hamburg, fluctuated within "silver points" (Flandreau [1996c]). Calling eG the number of Francs per Pound, and eS the number of Francs per Mark, and assuming, for the sake of simplicity, that (a) the cost of shipping from France is equal to the cost of shipping to France, and (b) the cost of shipping gold is equal to the cost of shipping silver, we can write in logs:
-c eG c (1.1)
-c eS c (1.2)
From equations (1.1) and (1.2) one gets:
- 2 pS 2c (2)
where pS = eG - eS is the number of marks per pound, or equivalently, the gold-silver price ratio which turns out to be kept within what may be called "gold-silver points". Given the normalization adopted, the center of the band coincides with the legal ratio (pS=0), while the gold-silver points correspond to levels of the gold-silver price ratio that trigger "bimetallic arbitrage". Indeed pS cannot fall under -2c, otherwise it would pay to import gold to France and ship silver to Hamburg. And pS cannot go beyond 2c otherwise a symmetrical arbitrage would occur. Hence, when shipping costs are considered, bimetallic arbitrage arises only as a limiting case.
The framework we use is based on the monetary model that has been extensively used in target zone literature. The dynamics of the bilateral exchange rates are described in equation (3), which gives the exchange rate as a function of their expected rate of change and of the "fundamentals" interpreted as the relative money supplies (fGt=mBt-mGt and fSt=mBt-mSt, mit i=B,S,G, being money supply in the Bimetallic, Silver, or Gold country):
eGt = fGt + a (E{deGt}/dt) (3)
eSt = fSt + a (E{deSt}/dt)
The factors driving money supplies include exogenous monetary shocks and endogenous elements resulting from bullion shipments. It is convenient to think of this mechanism in terms of the Humean price-specie flows mechanism (Hume [1752]). Suppose for instance that gold supply shocks take place in the gold country. This drives up British money supply and prices, and depreciates the exchange rate. There is, however, a level at which the imbalance between the pound and the franc is so large that residents of Britain find profitable to ship gold to France, in exchange for say, goods or capital. It is thus natural to think of money supplies in the three countries as being "regulated" through shipments that take place each time money stocks reach certain trigger levels, to be computed. The fundamentals' dynamics are thus written in vectorial form as (4):
dft = M.dt + S.dzt + B{dLt - dUt} (4)
where the first two terms on the right hand side correspond to exogenous shocks while the third element correspond to bullion shipments: dU is a shipment out of France, while dL is a shipment into France. And:
NOT AVAILABLE (5)
Where bG (resp bS) represents the relative size of the gold (resp. silver) economy with respect to the bimetallic economy. Matrix B reveals an interesting pattern: bullion shipments between, say, France and England do not merely influence these two countries' relative money supplies. They also influence the Franco-German relative money supplies. This is because gold flows from England to France cause the French money supply to rise with respect to Germany's as well. Of course, this effect will depend on the relative size of the various economies. If the bimetallic economy is very large, shipments to that economy will have negligible effects on its money supply.
The solution (derived in detail in the paper)to the problem described by (3) and (4) is the following: Relative money supplies can move within a parallelogram of the type represented in Figure 1. When they reach some boundary, a bullion shipment occurs from France or to France. There are two boundaries corresponding to gold shipments, and two boundaries corresponding to silver shipments. At the corners where boundaries intersect either cross shipments (one metal in the other out) or joint shipments (both metals either in or out) occur. Sterling exchange rates take values within [-c, c], and of course, the gold-silver price ratio takes values within [-2c, 2c]. Formulas for all relevant exchange rates are given in the paper.

Section III. The Mechanics of Bimetallism
Our model has a number of important predictions:
1) For a bimetallic system to be effective, one does not need the gold-silver price ratio to be pegged to the legal ratio. Indeed, our model shows that, due to arbitrage costs, the London price of silver (equivalently the gold-silver exchange rate) can fluctuate around the legal ratio.
2) The fluctuations of the gold silver price ratio are in fact part of the equilibration process. To see this, consider for instance the impact of repeated gold shocks. These will increase the money supply in England, and thus depreciate "sterling" exchange rates both vis--vis the franc and the mark. Hence gold supply shocks depreciate the gold-silver price ratio. This depreciation however, cannot go forever (contrary to what would have taken place had there not been a legal ratio), because at some point, some boundary on the fundamentals will be reached, triggering in turn a bullion shipment (from France or to France as we shall see below). In other words, the flexibility of the gold-silver price ratio is an essential ingredient of the adjustment mechanism.
3) Contrary to what Oppers has claimed, nothing can be learned from regressing sterling exchange rates on the gold silver price ratio. This is because all exchange rates are variables that depend upon the same fundamentals (the relative money supplies). The correlation between eG and pS cannot thus be interpreted as an estimate of the share of gold holdings in the bimetallic country's money supply: the correlation only reflects common underlying shocks and specific functional forms. (Recall that Oppers' regression may be written as eGt= X+(1-X )pSt+t where t is a white noise and X is the share of gold in the bimetallic economy).
4) Bimetallic arbitrage is NOT the essential mechanism through which the stabilization of the gold-silver price ratio is achieved, or equivalently, only under some special assumptions does the gold-silver price ratio reach its [-2c, 2c] boundaries. To see this, recall that bimetallic arbitrages take place when the gold-silver price ratio reaches -2c or 2c. For this to happen one must have the franc-sterling exchange rate and the franc-mark exchange rate reaching simultaneously opposite boundaries (-c and c). Suppose for instance that the franc-sterling exchange rate is at its highest level (c), while the franc-mark exchange rate is at its lowest level (-c). A positive money supply shock in Germany will require shipping silver to France: but this, by depreciating the franc will send it out of the gold points, which is not possible. Rational speculators realize this and consistently step in and ship bullion before the boundaries on the gold-silver price ratio are actually reached. Hence except in the limiting case where the bimetallic economy is infinitely large (implying in the above example that shipping silver to France will not send the franc out of the gold points thus precluding speculative shipments), the gold-silver price ratio will NOT expand over its entire range, and bimetallic arbitrage will NOT take place.
5) The larger the bimetallic economy (relative to other economies), the larger the interval within which the gold-silver price ratio can move. This seemingly counterintuitive result is a direct consequence of the previous point: as the relative size of the bimetallic economy decreases, its buffer role in the wake of bullion shipments diminishes. This requires speculative shipments to take place earlier, thus reducing the scope for fluctuations of the gold-silver price ratio. But a larger bimetallic economy has also presumably larger gold and silver reserves, and can thus operate its assigned stabilization scheme longer. Hence wider fluctuations of the gold-silver price ratio turn out to be an index of longevity, not of fragility! The knife-edge view is on its head!
6.1) Gresham's Law 1: The bad money may drive out the good. This is illustrated by Figure 1. Consider the sequence of gold discoveries that drives the Franco-British relative money supplies from A through B to C. At point C, the imbalance is such that a gold shipment to France takes place. As a result, fundamentals "jump" to point D, which is located on a (marginally) higher line than A. As dramatized in Figure 1, this increases the likelihood of future silver shipments, because fundamentals approach the silver exports boundary.
6.2) Gresham's Law 2: The good money may suck in the bad. Consider now the sequence of gold discoveries that drives fundamentals from A' through B' to C', where a silver export from France to Germany takes place. In this case, gold supply shocks may drive silver out of France, without gold being even imported there. The rationale for this paradoxical result is that repeated gold supply shocks are expected to "contaminate" the bimetallic country and thus depreciate its exchange rate vis--vis silver countries. Silver becomes cheaper in France. Hence silver may have to be shipped to Germany before gold is shipped to France. Note also that, because the shipment sends fundamentals towards D', the likelihood of future gold imports is increased.
7) If shocks in bullion markets dominate, the stationary distribution for the gold-silver exchange rate will display two peaks located respectively above and under the legal ratio. This is consistent with the observed persistence of the price ratio either above or under the legal ratio. The rationale for this is quite intuitive: repeated bullion supply shocks (gold or silver) tend to drive fundamentals towards points s2 and s4 in Figure 1 (because of 6.1 and 6.2), and these points are associated with exchange rates that are located strictly above or under the legal ratio. The observed persistence of the gold-silver exchange rate is thus fully supported by our model.

Conclusion
The paper constructs and solves a model of bimetallism which seeks to explain the dynamics of the gold-silver price ratio. Taking into account the existence of shipping costs, it demonstrates that, contrary to a view held by knife-edge theorists, movements away from the legal ratio are really part of the equilibration process. Second, it demonstrates that bimetallic arbitrage is not the main (let alone the only) way through which equilibration is achieved. Third, it shows that this implies some refinements of traditional interpretations of bimetallism as a case of Gresham's Law: the link between imports of the bad currency and exports of the good one is probabilistic, not deterministic. Finally, it shows that repeated bullion supply shocks produce persistence of the gold-silver price ratio either above or under the legal ratio - exactly as empirically observed. We hope that these theoretical findings can contribute to a substantial clarification of the recent debates about bimetallism.

References
Fisher, Irving [1926], The Purchasing Power of Money, Revised edition, New York, Macmillan.
Flandreau, Marc, [1995], "Coin Memories: New Estimates of French Metallic Currency 1840-1878", The Journal of European Economic History.
Flandreau, Marc, [1996a], "The French Crime of 1873: An Essay on the Emergence of the International Gold Standard", Journal of Economic History.
Flandreau, Marc [1996b], "Adjusting to the Gold Rush: Endogenous Bullion Points and the French Balance of Payments", Explorations in Economic History, pp. 417-439.
Flandreau, Marc, [1997], "Bimetallism in Equilibrium", in L. Officer et al. Monetary Standards in History, Routledge.
Friedman, M. [1990a], "Bimetallism Revisited", Journal of Economic Perspectives, 4 (4), 85-104.
Friedman, M. [1990b], "The Crime of 1873", Journal of Political Economy, 98 (6).
Garber, P., [1986], "Nominal Contracts in a Bimetallic Standard", American Economic Review, December, Vol 76, 5, 1012-1030.
Garber, P. and S. Weisrod, [1992] The Economics of Banking, Liquidity, and Money, Lexington: DC Heath and C.
Hume, D., "On the Balance of Trade", 1752, reprinted in Eichengreen and Flandreau, eds. The Gold Standard in Theory and History, 2nd ed., London, Routledge.
Oppers, S., [1992], "A Model of Bimetallism", mimeo, The University of Michigan.
Oppers, S., [1994], "Arbitrage in Bimetallic Money Supplies: Evidence from the exchange rate", mimeo, The University of Michigan.

FIGURE 1
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